%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL947^10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n005.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 08:14:18 AM UTC 2026
% Result : Theorem 7.86s 3.07s
% Output : Refutation 7.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 26
% Syntax : Number of formulae : 48 ( 11 unt; 0 typ; 6 def)
% Number of atoms : 523 ( 6 equ; 0 cnn)
% Maximal formula atoms : 44 ( 10 avg)
% Number of connectives : 1155 ( 2 ~; 3 |; 16 &; 942 @)
% ( 0 <=>; 192 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 14 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 2 con; 0-3 aty)
% Number of variables : 236 ( 58 ^; 176 !; 2 ?; 236 :)
% 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(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(mbox_decl,type,
mbox: ( 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(qmltpeq_decl,type,
qmltpeq: $i > $i > mworld > $o ).
thf(member_decl,type,
member: $i > $i > mworld > $o ).
thf(subset_decl,type,
subset: $i > $i > mworld > $o ).
thf(union_decl,type,
union: $i > $i > $i ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
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(mbox_def,definition,
( mbox
= ( ^ [A: mworld > $o,B: mworld] :
! [C: mworld] :
( ( mrel @ B @ C )
=> ( A @ C ) ) ) ) ).
thf(mforall_di_def,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
! [C: $i] :
( ( eiw_di @ C @ B )
=> ( A @ C @ B ) ) ) ) ).
thf(17,axiom,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_nonempty) ).
thf(142,plain,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ B @ C ) ) ) @ ( mbox @ ( qmltpeq @ A @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(42,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ( eiw_di @ F @ E )
=> ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
& ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ D @ F @ H ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ F @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mand @ ( mbox @ ( subset @ A @ B ) ) @ ( mbox @ ( subset @ B @ A ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( subset @ A @ B ) ) @ ( mbox @ ( subset @ B @ A ) ) ) @ ( mbox @ ( qmltpeq @ A @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
thf(52,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ( ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( subset @ B @ D @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ( subset @ D @ B @ F ) ) ) ) )
& ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( subset @ B @ D @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ( subset @ D @ B @ F ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mand
@ ( mbox
@ ( mimplies @ ( mbox @ ( subset @ A @ B ) )
@ ( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( member @ C @ A ) ) @ ( mbox @ ( member @ C @ B ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( member @ C @ A ) ) @ ( mbox @ ( member @ C @ B ) ) ) ) ) )
@ ( mbox @ ( subset @ A @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(84,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ( ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( subset @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ! [G: $i] :
( ( eiw_di @ G @ F )
=> ! [H: mworld] :
( ( mrel @ F @ H )
=> ( ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ B @ I ) )
=> ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ D @ I ) ) ) ) ) ) ) )
& ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ! [G: $i] :
( ( eiw_di @ G @ F )
=> ! [H: mworld] :
( ( mrel @ F @ H )
=> ( ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ B @ I ) )
=> ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ D @ I ) ) ) ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( subset @ B @ D @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(14,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( member @ C @ A ) ) ) @ ( mbox @ ( member @ C @ B ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_substitution_2) ).
thf(102,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ( eiw_di @ F @ E )
=> ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
& ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ B @ H ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ D @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( qmltpeq @ A @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(34,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ( qmltpeq @ B @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( qmltpeq @ ( union @ A @ A ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idempotency_of_union) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( qmltpeq @ ( union @ A @ A ) @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(22,plain,
~ ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ( qmltpeq @ ( union @ B @ B ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( subset @ C @ A ) ) ) @ ( mbox @ ( subset @ C @ B ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_substitution_2) ).
thf(144,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ( eiw_di @ F @ E )
=> ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
& ! [H: mworld] :
( ( mrel @ G @ H )
=> ( subset @ F @ B @ H ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( subset @ F @ D @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_substitution_1) ).
thf(108,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ( eiw_di @ F @ E )
=> ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( union @ B @ F ) @ ( union @ D @ F ) @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(16,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mand
@ ( mbox
@ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) )
@ ( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ C @ A ) ) @ ( mbox @ ( member @ C @ B ) ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ ( member @ C @ B ) ) @ ( mbox @ ( member @ C @ A ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ C @ A ) ) @ ( mbox @ ( member @ C @ B ) ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ ( member @ C @ B ) ) @ ( mbox @ ( member @ C @ A ) ) ) ) ) ) )
@ ( mbox @ ( qmltpeq @ A @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
thf(112,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ( ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ! [G: $i] :
( ( eiw_di @ G @ F )
=> ( ! [H: mworld] :
( ( mrel @ F @ H )
=> ( ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ B @ I ) )
=> ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ D @ I ) ) ) )
& ! [H: mworld] :
( ( mrel @ F @ H )
=> ( ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ D @ I ) )
=> ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ B @ I ) ) ) ) ) ) ) ) )
& ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ! [G: $i] :
( ( eiw_di @ G @ F )
=> ( ! [H: mworld] :
( ( mrel @ F @ H )
=> ( ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ B @ I ) )
=> ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ D @ I ) ) ) )
& ! [H: mworld] :
( ( mrel @ F @ H )
=> ( ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ D @ I ) )
=> ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ B @ I ) ) ) ) ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(20,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( member @ A @ C ) ) ) @ ( mbox @ ( member @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_substitution_1) ).
thf(154,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ( eiw_di @ F @ E )
=> ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
& ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ B @ F @ H ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ D @ F @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(12,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( qmltpeq @ ( union @ A @ B ) @ ( union @ B @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(82,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ( qmltpeq @ ( union @ B @ D ) @ ( union @ D @ B ) @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: mworld] : ( mrel @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(68,plain,
! [A: mworld] : ( mrel @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ A @ B )
& ( mrel @ B @ C ) )
=> ( mrel @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_transitive) ).
thf(28,plain,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ A @ B )
& ( mrel @ B @ C ) )
=> ( mrel @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(21,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( subset @ A @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(160,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ( subset @ B @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(11,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ C @ ( union @ A @ B ) ) ) @ ( mor @ ( mbox @ ( member @ C @ A ) ) @ ( mbox @ ( member @ C @ B ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ ( member @ C @ A ) ) @ ( mbox @ ( member @ C @ B ) ) ) @ ( mbox @ ( member @ C @ ( union @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
thf(70,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ( eiw_di @ F @ E )
=> ( ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ ( union @ B @ D ) @ H ) )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ B @ H ) )
| ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ D @ H ) ) ) ) )
& ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ B @ H ) )
| ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ D @ H ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ ( union @ B @ D ) @ H ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_substitution_2) ).
thf(48,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ( eiw_di @ F @ E )
=> ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( union @ F @ B ) @ ( union @ F @ D ) @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ B @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(150,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ D @ B @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(6,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( subset @ A @ C ) ) ) @ ( mbox @ ( subset @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_substitution_1) ).
thf(36,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ( eiw_di @ F @ E )
=> ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
& ! [H: mworld] :
( ( mrel @ G @ H )
=> ( subset @ B @ F @ H ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( subset @ D @ F @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( subset @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( union @ A @ B ) @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_union) ).
thf(30,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( subset @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ ( union @ B @ D ) @ D @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(239,plain,
$false,
inference(e,[status(thm)],[142,42,52,84,102,34,22,144,108,112,154,82,68,28,160,70,48,150,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL947^10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % Computer : n005.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 10:46:31 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.86/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.57/1.05 % [INFO] Parsing done (272ms).
% 1.57/1.07 % [INFO] Running in sequential loop mode.
% 2.40/1.47 % [INFO] eprover registered as external prover.
% 2.40/1.48 % [INFO] Scanning for conjecture ...
% 2.85/1.62 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 3.06/1.70 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 3.06/1.75 % [INFO] Problem is higher-order (TPTP THF).
% 3.06/1.76 % [INFO] Type checking passed.
% 3.06/1.77 % [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 ...
% 7.86/3.06 % External prover 'e' found a proof!
% 7.86/3.06 % [INFO] Killing All external provers ...
% 7.86/3.06 % Time passed: 2724ms (effective reasoning time: 1992ms)
% 7.86/3.06 % 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)>
% 7.86/3.07 % Axioms used in derivation (19): member_substitution_1, reflexivity_of_subset, equal_member_defn, union_substitution_2, eiw_di_nonempty, subset_union, member_substitution_2, symmetry, mrel_reflexive, subset_substitution_2, reflexivity, commutativity_of_union, subset_substitution_1, union_substitution_1, mrel_transitive, equal_defn, transitivity, union_defn, subset_defn
% 7.86/3.07 % No. of inferences in proof: 42
% 7.86/3.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2724 ms resp. 1992 ms w/o parsing
% 7.86/3.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.86/3.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------