%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NLP266^23 : 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 : n004.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 08:16:18 AM UTC 2026
% Result : Theorem 34.97s 7.61s
% Output : Refutation 34.97s
% 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 : 129 ( 6 equ; 0 cnn)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 265 ( 2 ~; 0 |; 19 &; 221 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 4 con; 0-4 aty)
% Number of variables : 71 ( 30 ^; 31 !; 10 ?; 71 :)
% 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(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(u_decl,type,
u: $i ).
thf(one_decl,type,
one: $i ).
thf(number_decl,type,
number: $i > $i > mworld > $o ).
thf(string_decl,type,
string: $i > mworld > $o ).
thf(in_decl,type,
in: $i > $i > $i > mworld > $o ).
thf(do_decl,type,
do: $i > $i > $i > mworld > $o ).
thf(entry_box_decl,type,
entry_box: $i > mworld > $o ).
thf(userid_decl,type,
userid: $i > $i > mworld > $o ).
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(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
@ ( mexists_di
@ ^ [A: $i] :
( mexists_di
@ ^ [B: $i] :
( mexists_di
@ ^ [C: $i] :
( mexists_di
@ ^ [D: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ A ) @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [E: $i] : ( mimplies @ ( do @ D @ C @ E ) @ ( in @ A @ B @ E ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [A: $i] :
( mexists_di
@ ^ [B: $i] :
( mexists_di
@ ^ [C: $i] :
( mexists_di
@ ^ [D: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ A ) @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [E: $i] : ( mimplies @ ( do @ D @ C @ E ) @ ( in @ A @ B @ E ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ? [B: $i] :
( ( eiw_di @ B @ A )
& ? [C: $i] :
( ( eiw_di @ C @ A )
& ? [D: $i] :
( ( eiw_di @ D @ A )
& ? [E: $i] :
( ( eiw_di @ E @ A )
& ! [F: mworld] :
( ( mrel @ A @ F )
=> ( ( userid @ u @ B @ F )
& ( entry_box @ C @ F )
& ( number @ C @ one @ F ) ) )
& ! [F: mworld] :
( ( mrel @ A @ F )
=> ! [G: $i] :
( ( eiw_di @ G @ F )
=> ( ( do @ E @ D @ G @ F )
=> ( in @ B @ C @ G @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ A @ C )
& ( mrel @ A @ B ) )
=> ( mrel @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_euclidean) ).
thf(21,plain,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ A @ C )
& ( mrel @ A @ B ) )
=> ( mrel @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
( mlocal
@ ( mexists_di
@ ^ [A: $i] : ( mbox @ ( mand @ ( entry_box @ A ) @ ( number @ A @ one ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(32,plain,
? [A: $i] :
( ( eiw_di @ A @ mactual )
& ! [B: mworld] :
( ( mrel @ mactual @ B )
=> ( ( entry_box @ A @ B )
& ( number @ A @ one @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,axiom,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [A: $i] : ( mbox @ ( mand @ ( userid @ u @ A ) @ ( string @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(27,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ? [B: $i] :
( ( eiw_di @ B @ A )
& ! [C: mworld] :
( ( mrel @ A @ C )
=> ( ( userid @ u @ B @ C )
& ( string @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,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)],[5]) ).
thf(3,axiom,
! [A: mworld] : ( mrel @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(19,plain,
! [A: mworld] : ( mrel @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mimplies @ ( mand @ ( string @ B ) @ ( entry_box @ C ) )
@ ( mexists_di
@ ^ [D: $i] :
( mbox
@ ( mforall_di
@ ^ [E: $i] : ( mimplies @ ( do @ A @ D @ E ) @ ( in @ B @ C @ E ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(37,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: $i] :
( ( eiw_di @ C @ A )
=> ! [D: $i] :
( ( eiw_di @ D @ A )
=> ( ( ( string @ C @ A )
& ( entry_box @ D @ A ) )
=> ? [E: $i] :
( ( eiw_di @ E @ A )
& ! [F: mworld] :
( ( mrel @ A @ F )
=> ! [G: $i] :
( ( eiw_di @ G @ F )
=> ( ( do @ B @ E @ G @ F )
=> ( in @ C @ D @ G @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,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(25,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)],[6]) ).
thf(13074,plain,
$false,
inference(e,[status(thm)],[10,21,32,27,23,19,37,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NLP266^23 : 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
% 0.09/0.22 % Computer : n004.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 11:44:52 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 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
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.52/1.03 % [INFO] Parsing done (224ms).
% 1.52/1.05 % [INFO] Running in sequential loop mode.
% 2.17/1.45 % [INFO] eprover registered as external prover.
% 2.17/1.46 % [INFO] Scanning for conjecture ...
% 2.59/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.59/1.64 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.59/1.66 % [INFO] Problem is higher-order (TPTP THF).
% 2.59/1.66 % [INFO] Type checking passed.
% 2.59/1.67 % [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 ...
% 34.97/7.60 % External prover 'e' found a proof!
% 34.97/7.60 % [INFO] Killing All external provers ...
% 34.97/7.61 % Time passed: 7234ms (effective reasoning time: 6554ms)
% 34.97/7.61 % 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)>
% 34.97/7.61 % Axioms used in derivation (7): mrel_euclidean, mrel_reflexive, ax1, eiw_di_nonempty, ax2, ax3, eiw_di_decr
% 34.97/7.61 % No. of inferences in proof: 18
% 34.97/7.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7234 ms resp. 6554 ms w/o parsing
% 34.97/7.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 34.97/7.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------