%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL579^2 : TPTP v9.3.1. Released v5.1.0.
% 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 : n009.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 08:14:05 AM UTC 2026
% Result : Theorem 4.02s 2.29s
% Output : Refutation 4.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 21 ( 10 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 57 ( 14 ~; 5 |; 2 &; 26 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 3 usr; 5 con; 0-2 aty)
% Number of variables : 9 ( 0 ^; 8 !; 0 ?; 9 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(cY_decl,type,
cY: $i ).
thf(cX_decl,type,
cX: $i ).
thf(sk1_decl,type,
sk1: $i > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $o] :
~ ( ( A @ cX )
=> ( A @ cY ) ) ) ) ).
thf(1,conjecture,
( ! [A: $i > $o] :
( ( A @ cY )
=> ( A @ cX ) )
=> ! [A: $i > $o] :
( ( A @ cX )
=> ( A @ cY ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM76A) ).
thf(2,negated_conjecture,
~ ( ! [A: $i > $o] :
( ( A @ cY )
=> ( A @ cX ) )
=> ! [A: $i > $o] :
( ( A @ cX )
=> ( A @ cY ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i > $o] :
( ( A @ cY )
=> ( A @ cX ) )
=> ! [A: $i > $o] :
( ( A @ cX )
=> ( A @ cY ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: $i > $o] :
( ( ~ ( A @ cY )
| ( A @ cX ) )
& ( sk1 @ cX )
& ~ ( sk1 @ cY ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
sk1 @ cX,
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
~ ( sk1 @ cY ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
( ~ $true
| ( ( sk1 @ cX )
!= ( sk1 @ cY ) ) ),
inference(paramod_ordered,[status(thm)],[6,7]) ).
thf(12,plain,
( ( sk1 @ cX )
!= ( sk1 @ cY ) ),
inference(simp,[status(thm)],[11]) ).
thf(13,plain,
cX != cY,
inference(simp,[status(thm)],[12]) ).
thf(5,plain,
! [A: $i > $o] :
( ~ ( A @ cY )
| ( A @ cX ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
( ( cY != cY )
| ( cY = cX ) ),
inference(replace_leibeq,[status(thm)],[5:[bind(A,$thf( (=) @ $i @ cY ))]]) ).
thf(9,plain,
( ( cY != cY )
| ( cX = cY ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(10,plain,
cX = cY,
inference(simp,[status(thm)],[9]) ).
thf(15,plain,
cY != cY,
inference(rewrite,[status(thm)],[13,10]) ).
thf(16,plain,
$false,
inference(simp,[status(thm)],[15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL579^2 : TPTP v9.3.1. Released v5.1.0.
% 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
% 0.10/0.27 % Computer : n009.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Tue Sep 29 08:54:45 UTC 2026
% 0.27/0.27 % CPUTime :
% 0.27/0.27 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
% 1.10/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.33/0.99 % [INFO] Parsing done (147ms).
% 1.33/1.00 % [INFO] Running in sequential loop mode.
% 2.05/1.35 % [INFO] eprover registered as external prover.
% 2.05/1.36 % [INFO] Scanning for conjecture ...
% 2.29/1.46 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.51/1.50 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.51/1.50 % [INFO] Problem is higher-order (TPTP THF).
% 2.51/1.51 % [INFO] Type checking passed.
% 2.51/1.52 % [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 ...
% 4.02/2.28 % [INFO] Killing All external provers ...
% 4.02/2.29 % Time passed: 1819ms (effective reasoning time: 1277ms)
% 4.02/2.29 % 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)>
% 4.02/2.29 % Axioms used in derivation (0):
% 4.02/2.29 % No. of inferences in proof: 15
% 4.02/2.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1819 ms resp. 1277 ms w/o parsing
% 4.37/2.37 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.37/2.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------