%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL953^8 : 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 : n016.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 3.95s 2.35s
% Output : Refutation 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 24 ( 11 unt; 0 typ; 6 def)
% Number of atoms : 139 ( 6 equ; 0 cnn)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 267 ( 7 ~; 0 |; 3 &; 216 @)
% ( 0 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 2 con; 0-3 aty)
% Number of variables : 69 ( 24 ^; 40 !; 5 ?; 69 :)
% 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(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(in_decl,type,
in: $i > $i > mworld > $o ).
thf(disjoint_decl,type,
disjoint: $i > $i > mworld > $o ).
thf(empty_decl,type,
empty: $i > mworld > $o ).
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(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(1,conjecture,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ A @ B ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ A ) @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_zfmisc_1) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ A @ B ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ A ) @ B ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,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 )
=> ~ ! [G: mworld] :
( ( mrel @ F @ G )
=> ( in @ B @ D @ G ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( disjoint @ ( singleton @ B ) @ D @ 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 @ ( mimplies @ ( mbox @ ( disjoint @ A @ B ) ) @ ( mbox @ ( disjoint @ B @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(25,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 )
=> ( disjoint @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( disjoint @ D @ B @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(29,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)],[6]) ).
thf(3,axiom,
! [A: mworld] : ( mrel @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(21,plain,
! [A: mworld] : ( mrel @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( in @ A @ B ) ) ) ) @ ( mbox @ ( disjoint @ ( singleton @ A ) @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_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: mworld] :
( ( mrel @ E @ F )
=> ~ ! [G: mworld] :
( ( mrel @ F @ G )
=> ( in @ B @ D @ G ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( disjoint @ ( singleton @ B ) @ D @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(8,axiom,
( mlocal
@ ( mexists_di
@ ^ [A: $i] : ( mbox @ ( mnot @ ( mbox @ ( empty @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(39,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)],[8]) ).
thf(7,axiom,
( mlocal
@ ( mexists_di
@ ^ [A: $i] : ( mbox @ ( empty @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(35,plain,
? [A: $i] :
( ( eiw_di @ A @ mactual )
& ! [B: mworld] :
( ( mrel @ mactual @ B )
=> ( empty @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_nonempty) ).
thf(23,plain,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(49,plain,
$false,
inference(e,[status(thm)],[10,25,29,21,44,39,35,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL953^8 : 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 : n016.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 10:57:49 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
% 0.99/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/1.03 % [INFO] Parsing done (213ms).
% 1.43/1.04 % [INFO] Running in sequential loop mode.
% 2.02/1.43 % [INFO] eprover registered as external prover.
% 2.02/1.44 % [INFO] Scanning for conjecture ...
% 2.22/1.57 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.40/1.60 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.40/1.62 % [INFO] Problem is higher-order (TPTP THF).
% 2.40/1.62 % [INFO] Type checking passed.
% 2.40/1.63 % [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 ...
% 3.95/2.35 % External prover 'e' found a proof!
% 3.95/2.35 % [INFO] Killing All external provers ...
% 3.95/2.35 % Time passed: 1961ms (effective reasoning time: 1300ms)
% 3.95/2.35 % 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)>
% 3.95/2.35 % Axioms used in derivation (7): mrel_reflexive, l28_zfmisc_1, eiw_di_nonempty, rc1_xboole_0, symmetry_r1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden
% 3.95/2.35 % No. of inferences in proof: 18
% 3.95/2.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1961 ms resp. 1300 ms w/o parsing
% 4.27/2.42 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.27/2.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------