%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO928^1 : TPTP v9.3.1. Released v9.0.0.
% 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 : n005.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 08:46:14 AM UTC 2026
% Result : Theorem 2.91s 1.48s
% Output : Refutation 3.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 10 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 34 ( 2 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 76 ( 2 ~; 0 |; 2 &; 58 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 9 ^; 17 !; 2 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mrel_decl,type,
mrel: mworld > mworld > $o ).
thf(mbox_decl,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(mactual_decl,type,
mactual: mworld ).
thf(mlocal_decl,type,
mlocal: ( mworld > $o ) > $o ).
thf(f_decl,type,
f: mworld > $i > $o ).
thf(eiw_di_decl,type,
eiw_di: $i > mworld > $o ).
thf(mbox_def,definition,
( mbox
= ( ^ [A: mworld > $o,B: mworld] :
! [C: mworld] :
( ( mrel @ B @ C )
=> ( A @ C ) ) ) ) ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(1,conjecture,
( mlocal
@ ^ [A: mworld] :
( ! [B: $i] :
( ( eiw_di @ B @ A )
=> ( mbox
@ ^ [C: mworld] : ( f @ C @ B )
@ A ) )
=> ( mbox
@ ^ [B: mworld] :
! [C: $i] :
( ( eiw_di @ C @ B )
=> ( f @ B @ C ) )
@ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',barcan_formula) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ^ [A: mworld] :
( ! [B: $i] :
( ( eiw_di @ B @ A )
=> ( mbox
@ ^ [C: mworld] : ( f @ C @ B )
@ A ) )
=> ( mbox
@ ^ [B: mworld] :
! [C: $i] :
( ( eiw_di @ C @ B )
=> ( f @ B @ C ) )
@ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ( ! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: mworld] :
( ( mrel @ mactual @ B )
=> ( f @ B @ A ) ) )
=> ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ( f @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_nonempty) ).
thf(11,plain,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: mworld,B: mworld,C: $i] :
( ( ( eiw_di @ C @ A )
& ( mrel @ B @ A ) )
=> ( eiw_di @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_decr) ).
thf(13,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)],[4]) ).
thf(15,plain,
$false,
inference(e,[status(thm)],[5,11,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO928^1 : TPTP v9.3.1. Released v9.0.0.
% 0.00/0.08 % 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
% 0.10/0.22 % Computer : n005.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 17:27:46 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 0.65/0.53 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.99/0.63 % [INFO] Parsing done (93ms).
% 0.99/0.64 % [INFO] Input problem is non-classical (logic $modal). Running HOL transformation from semantics specification contained in the problem file ...
% 1.13/0.71 % [INFO] Running in sequential loop mode.
% 1.68/0.90 % [INFO] eprover registered as external prover.
% 1.68/0.90 % [INFO] Scanning for conjecture ...
% 1.68/0.95 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.68/0.98 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.68/0.99 % [INFO] Problem is higher-order (TPTP THF).
% 1.68/0.99 % [INFO] Type checking passed.
% 1.68/1.00 % [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 ...
% 2.91/1.47 % External prover 'e' found a proof!
% 2.91/1.47 % [INFO] Killing All external provers ...
% 2.91/1.47 % Time passed: 1154ms (effective reasoning time: 757ms)
% 2.91/1.47 % 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)>
% 2.91/1.48 % Axioms used in derivation (2): eiw_di_nonempty, eiw_di_decr
% 2.91/1.48 % No. of inferences in proof: 8
% 2.91/1.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1154 ms resp. 757 ms w/o parsing
% 3.17/1.53 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.17/1.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------