%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL952^12 : 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 : n011.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 08:14:19 AM UTC 2026
% Result : Theorem 5.18s 2.24s
% Output : Refutation 5.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 25
% Syntax : Number of formulae : 45 ( 12 unt; 0 typ; 7 def)
% Number of atoms : 348 ( 7 equ; 0 cnn)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 751 ( 5 ~; 0 |; 8 &; 616 @)
% ( 0 <=>; 122 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 12 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 2 con; 0-3 aty)
% Number of variables : 172 ( 51 ^; 116 !; 5 ?; 172 :)
% 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(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(mexists_di_decl,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(qmltpeq_decl,type,
qmltpeq: $i > $i > mworld > $o ).
thf(in_decl,type,
in: $i > $i > mworld > $o ).
thf(empty_decl,type,
empty: $i > mworld > $o ).
thf(set_intersection2_decl,type,
set_intersection2: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $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(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(mexists_di_def,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
? [C: $i] :
( ( eiw_di @ C @ B )
& ( A @ C @ B ) ) ) ) ).
thf(6,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( qmltpeq @ A @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(42,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)],[6]) ).
thf(1,conjecture,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ A @ ( singleton @ B ) ) @ ( singleton @ B ) ) ) @ ( mbox @ ( in @ B @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_zfmisc_1) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ A @ ( singleton @ B ) ) @ ( singleton @ B ) ) ) @ ( mbox @ ( in @ B @ A ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(20,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 @ ( set_intersection2 @ B @ ( singleton @ D ) ) @ ( singleton @ D ) @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( in @ D @ B @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,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 @ ( set_intersection2 @ C @ A ) @ ( set_intersection2 @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_intersection2_substitution_2) ).
thf(38,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 @ ( set_intersection2 @ F @ B ) @ ( set_intersection2 @ F @ D ) @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,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 @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_intersection2_substitution_1) ).
thf(65,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 @ ( set_intersection2 @ B @ F ) @ ( set_intersection2 @ D @ F ) @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( qmltpeq @ ( set_intersection2 @ A @ A ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(77,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 @ ( set_intersection2 @ B @ B ) @ B @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(13,axiom,
( mlocal
@ ( mexists_di
@ ^ [A: $i] : ( mbox @ ( empty @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(73,plain,
? [A: $i] :
( ( eiw_di @ A @ mactual )
& ! [B: mworld] :
( ( mrel @ mactual @ B )
=> ( empty @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,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 @ ( in @ C @ A ) ) ) @ ( mbox @ ( in @ C @ B ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_substitution_2) ).
thf(32,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 )
=> ( in @ F @ B @ H ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( in @ F @ D @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
! [A: mworld,B: mworld] : ( mrel @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
thf(80,plain,
! [A: mworld,B: mworld] : ( mrel @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(8,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(50,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)],[8]) ).
thf(16,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_substitution_1) ).
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 )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ ( singleton @ B ) @ ( singleton @ D ) @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(3,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( qmltpeq @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ B @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
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 )
=> ( qmltpeq @ ( set_intersection2 @ B @ D ) @ ( set_intersection2 @ D @ B ) @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(19,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( in @ A @ B ) ) @ ( mbox @ ( mnot @ ( mbox @ ( in @ B @ A ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(94,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 )
=> ( in @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ~ ! [G: mworld] :
( ( mrel @ F @ G )
=> ( in @ D @ B @ G ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(12,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( set_intersection2 @ A @ ( singleton @ B ) ) @ ( singleton @ B ) ) ) @ ( mbox @ ( in @ B @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l30_zfmisc_1) ).
thf(69,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 @ ( set_intersection2 @ B @ ( singleton @ D ) ) @ ( singleton @ D ) @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( in @ D @ B @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
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 @ ( qmltpeq @ B @ C ) ) ) @ ( mbox @ ( qmltpeq @ A @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(88,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)],[18]) ).
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 @ ( in @ A @ C ) ) ) @ ( mbox @ ( in @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_substitution_1) ).
thf(44,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 )
=> ( in @ B @ F @ H ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( in @ D @ F @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( empty @ A ) ) ) @ ( mbox @ ( empty @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_substitution_1) ).
thf(59,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 )
=> ( empty @ B @ F ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( empty @ D @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
( mlocal
@ ( mexists_di
@ ^ [A: $i] : ( mbox @ ( mnot @ ( mbox @ ( empty @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(54,plain,
? [A: $i] :
( ( eiw_di @ A @ mactual )
& ! [B: mworld] :
( ( mrel @ mactual @ B )
=> ~ ! [C: mworld] :
( ( mrel @ B @ C )
=> ( empty @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(17,axiom,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_nonempty) ).
thf(86,plain,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(100,plain,
$false,
inference(e,[status(thm)],[42,20,38,65,77,73,32,80,50,82,30,94,69,88,44,59,54,86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL952^12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % 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
% 0.08/0.19 % Computer : n011.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 10:51:01 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 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
% 0.66/0.51 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.10/0.65 % [INFO] Parsing done (141ms).
% 1.10/0.66 % [INFO] Running in sequential loop mode.
% 1.81/0.95 % [INFO] eprover registered as external prover.
% 1.81/0.96 % [INFO] Scanning for conjecture ...
% 2.07/1.09 % [INFO] Found a conjecture (or negated_conjecture) and 17 axioms. Running axiom selection ...
% 2.29/1.17 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 2.48/1.21 % [INFO] Problem is higher-order (TPTP THF).
% 2.48/1.21 % [INFO] Type checking passed.
% 2.48/1.22 % [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 ...
% 5.18/2.23 % External prover 'e' found a proof!
% 5.18/2.23 % [INFO] Killing All external provers ...
% 5.18/2.23 % Time passed: 1943ms (effective reasoning time: 1569ms)
% 5.18/2.23 % 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)>
% 5.18/2.24 % Axioms used in derivation (17): in_substitution_2, idempotence_k3_xboole_0, empty_substitution_1, set_intersection2_substitution_2, eiw_di_nonempty, set_intersection2_substitution_1, in_substitution_1, rc1_xboole_0, transitivity, rc2_xboole_0, commutativity_k3_xboole_0, l30_zfmisc_1, reflexivity, mrel_universal, singleton_substitution_1, antisymmetry_r2_hidden, symmetry
% 5.18/2.24 % No. of inferences in proof: 38
% 5.18/2.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1943 ms resp. 1569 ms w/o parsing
% 5.56/2.34 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.56/2.34 % [INFO] Killing All external provers ...
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