%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL962^16 : 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 08:14:20 AM UTC 2026
% Result : Theorem 4.94s 2.60s
% Output : Refutation 5.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 12
% Syntax : Number of formulae : 22 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 64 ( 4 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 133 ( 7 ~; 0 |; 4 &; 108 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 32 ( 9 ^; 23 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mindex_type,type,
mindex: $tType ).
thf(mrel_decl,type,
mrel: mindex > mworld > mworld > $o ).
thf('#b_decl',type,
'#b': mindex ).
thf('#a_decl',type,
'#a': mindex ).
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: mindex > ( mworld > $o ) > mworld > $o ).
thf(p_decl,type,
p: mworld > $o ).
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: mindex,B: mworld > $o,C: mworld] :
! [D: mworld] :
( ( mrel @ A @ C @ D )
=> ( B @ D ) ) ) ) ).
thf(1,conjecture,
mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ( mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: mworld] :
( ( mrel @ '#a' @ mactual @ A )
=> ~ ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#b' @ p ) ) @ ( mbox @ '#a' @ ( mnot @ ( mbox @ '#b' @ p ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_axiom_2) ).
thf(24,plain,
( ~ ! [A: mworld] :
( ( mrel @ '#b' @ mactual @ A )
=> ( p @ A ) )
=> ! [A: mworld] :
( ( mrel @ '#a' @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ '#b' @ A @ B )
=> ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: mworld] : ( mrel @ '#b' @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#b_reflexive') ).
thf(14,plain,
! [A: mworld] : ( mrel @ '#b' @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ '#a' @ A @ B )
& ( mrel @ '#a' @ B @ C ) )
=> ( mrel @ '#a' @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#a_transitive') ).
thf(20,plain,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ '#a' @ A @ B )
& ( mrel @ '#a' @ B @ C ) )
=> ( mrel @ '#a' @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
mlocal @ ( mnot @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_a_axiom_1) ).
thf(28,plain,
~ ( p @ mactual ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
mlocal @ ( mbox @ '#a' @ ( mimplies @ p @ ( mbox @ '#b' @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_axiom_1) ).
thf(22,plain,
! [A: mworld] :
( ( mrel @ '#a' @ mactual @ A )
=> ( ( p @ A )
=> ! [B: mworld] :
( ( mrel @ '#b' @ A @ B )
=> ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: mworld] : ( mrel @ '#a' @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#a_reflexive') ).
thf(18,plain,
! [A: mworld] : ( mrel @ '#a' @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ '#b' @ A @ B )
& ( mrel @ '#b' @ B @ C ) )
=> ( mrel @ '#b' @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#b_transitive') ).
thf(16,plain,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ '#b' @ A @ B )
& ( mrel @ '#b' @ B @ C ) )
=> ( mrel @ '#b' @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(33,plain,
$false,
inference(e,[status(thm)],[10,24,14,20,28,22,18,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL962^16 : 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
% 0.09/0.23 % Computer : n016.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 11:04:38 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
% 1.20/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.86/1.21 % [INFO] Parsing done (236ms).
% 1.86/1.23 % [INFO] Running in sequential loop mode.
% 2.70/1.69 % [INFO] eprover registered as external prover.
% 2.95/1.70 % [INFO] Scanning for conjecture ...
% 3.17/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 3.17/1.86 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 3.17/1.88 % [INFO] Problem is higher-order (TPTP THF).
% 3.17/1.88 % [INFO] Type checking passed.
% 3.17/1.89 % [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 ...
% 4.94/2.59 % External prover 'e' found a proof!
% 4.94/2.59 % [INFO] Killing All external provers ...
% 4.94/2.60 % Time passed: 2155ms (effective reasoning time: 1360ms)
% 4.94/2.60 % 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)>
% 4.94/2.60 % Axioms used in derivation (7): mrel_#a_transitive, ab_axiom_2, mrel_#b_transitive, ab_axiom_1, mrel_#a_reflexive, mrel_#b_reflexive, not_a_axiom_1
% 4.94/2.60 % No. of inferences in proof: 18
% 4.94/2.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2155 ms resp. 1360 ms w/o parsing
% 5.31/2.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.31/2.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------