%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL956^18 : 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 : n006.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 4.55s 2.15s
% Output : Refutation 5.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 15 ( 10 unt; 0 typ; 5 def)
% Number of atoms : 105 ( 5 equ; 0 cnn)
% Maximal formula atoms : 30 ( 7 avg)
% Number of connectives : 169 ( 2 ~; 0 |; 13 &; 138 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 49 ( 19 ^; 23 !; 7 ?; 49 :)
% 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(mexists_di_decl,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(p_decl,type,
p: mworld > $o ).
thf(big_q_decl,type,
big_q: $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(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
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [A: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ A ) ) ) )
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [A: $i] : ( mbox @ ( big_q @ A ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [A: $i] : ( mbox @ ( big_q @ A ) ) ) )
@ ( mexists_di
@ ^ [A: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2109) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [A: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ A ) ) ) )
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [A: $i] : ( mbox @ ( big_q @ A ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [A: $i] : ( mbox @ ( big_q @ A ) ) ) )
@ ( mexists_di
@ ^ [A: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ A ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ? [B: $i] :
( ( eiw_di @ B @ A )
& ! [C: mworld] :
( ( mrel @ A @ C )
=> ( p @ C ) )
& ! [C: mworld] :
( ( mrel @ A @ C )
=> ( big_q @ B @ C ) ) )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( p @ B ) )
& ? [B: $i] :
( ( eiw_di @ B @ A )
& ! [C: mworld] :
( ( mrel @ A @ C )
=> ( big_q @ B @ C ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( p @ B ) )
& ? [B: $i] :
( ( eiw_di @ B @ A )
& ! [C: mworld] :
( ( mrel @ A @ C )
=> ( big_q @ B @ C ) ) ) )
=> ? [B: $i] :
( ( eiw_di @ B @ A )
& ! [C: mworld] :
( ( mrel @ A @ C )
=> ( p @ C ) )
& ! [C: mworld] :
( ( mrel @ A @ C )
=> ( big_q @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: mworld,B: mworld] : ( mrel @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
thf(35,plain,
! [A: mworld,B: mworld] : ( mrel @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_nonempty) ).
thf(37,plain,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: mworld,B: mworld,C: $i] :
( ( ( eiw_di @ C @ A )
& ( mrel @ A @ B ) )
=> ( eiw_di @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_cumul) ).
thf(39,plain,
! [A: mworld,B: mworld,C: $i] :
( ( ( eiw_di @ C @ A )
& ( mrel @ A @ B ) )
=> ( eiw_di @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(42,plain,
$false,
inference(e,[status(thm)],[6,35,37,39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL956^18 : 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 : n006.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 10:54:39 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
% 1.11/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.71/1.07 % [INFO] Parsing done (234ms).
% 1.71/1.09 % [INFO] Running in sequential loop mode.
% 2.65/1.52 % [INFO] eprover registered as external prover.
% 2.65/1.53 % [INFO] Scanning for conjecture ...
% 2.97/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.97/1.63 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.97/1.63 % [INFO] Problem is higher-order (TPTP THF).
% 2.97/1.63 % [INFO] Type checking passed.
% 2.97/1.64 % [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 ...
% 4.55/2.14 % External prover 'e' found a proof!
% 4.55/2.14 % [INFO] Killing All external provers ...
% 4.55/2.14 % Time passed: 1769ms (effective reasoning time: 1045ms)
% 4.55/2.14 % 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)>
% 4.55/2.14 % Axioms used in derivation (3): mrel_universal, eiw_di_nonempty, eiw_di_cumul
% 4.55/2.15 % No. of inferences in proof: 10
% 4.55/2.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1769 ms resp. 1045 ms w/o parsing
% 5.04/2.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.04/2.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------