%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PLA053^2 : 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 : n010.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 08:20:24 AM UTC 2026
% Result : Theorem 3.40s 1.56s
% Output : Refutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 18 ( 9 unt; 0 typ; 6 def)
% Number of atoms : 74 ( 6 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 114 ( 2 ~; 0 |; 4 &; 97 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 2 con; 0-3 aty)
% Number of variables : 39 ( 21 ^; 13 !; 5 ?; 39 :)
% 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(mforall_di_decl,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(mexists_di_decl,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(h_decl,type,
h: $i > mworld > $o ).
thf(bomb_decl,type,
bomb: $i > mworld > $o ).
thf(defused_decl,type,
defused: $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] : ( A @ C @ B ) ) ) ).
thf(mexists_di_def,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
? [C: $i] : ( A @ C @ B ) ) ) ).
thf(3,axiom,
! [A: mworld] : ( mrel @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(14,plain,
! [A: mworld] : ( mrel @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mexists_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mand @ ( bomb @ A ) @ ( h @ B ) ) @ ( defused @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(20,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
? [C: $i] :
! [D: mworld] :
( ( mrel @ A @ D )
=> ( ( ( bomb @ B @ D )
& ( h @ C @ D ) )
=> ( defused @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mexists_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( bomb @ A ) @ ( h @ B ) ) @ ( defused @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mexists_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( bomb @ A ) @ ( h @ B ) ) @ ( defused @ A ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
? [C: $i] :
( ( ( bomb @ B @ A )
& ( h @ C @ A ) )
=> ( defused @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
( mlocal
@ ( mexists_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( bomb @ B ) @ ( h @ A ) ) @ ( mbox @ ( bomb @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(18,plain,
? [A: $i] :
! [B: mworld] :
( ( mrel @ mactual @ B )
=> ! [C: $i] :
( ( ( bomb @ C @ B )
& ( h @ A @ B ) )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ( bomb @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
mlocal @ ( mbox @ ( mexists_di @ bomb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(16,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ? [B: $i] : ( bomb @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,plain,
$false,
inference(e,[status(thm)],[14,20,7,18,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PLA053^2 : 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
% 0.10/0.24 % Computer : n010.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Sep 29 13:21:03 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 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
% 0.94/0.64 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.14/0.76 % [INFO] Parsing done (123ms).
% 1.14/0.77 % [INFO] Running in sequential loop mode.
% 1.70/0.99 % [INFO] eprover registered as external prover.
% 1.70/1.00 % [INFO] Scanning for conjecture ...
% 2.05/1.07 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.05/1.09 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.05/1.09 % [INFO] Problem is higher-order (TPTP THF).
% 2.05/1.10 % [INFO] Type checking passed.
% 2.05/1.10 % [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 ...
% 3.40/1.56 % External prover 'e' found a proof!
% 3.40/1.56 % [INFO] Killing All external provers ...
% 3.40/1.56 % Time passed: 1174ms (effective reasoning time: 789ms)
% 3.40/1.56 % 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)>
% 3.40/1.56 % Axioms used in derivation (4): mrel_reflexive, ax3, ax2, ax1
% 3.40/1.56 % No. of inferences in proof: 12
% 3.40/1.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1174 ms resp. 789 ms w/o parsing
% 3.78/1.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.78/1.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------