%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG279^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 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 : n012.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 07:45:07 AM UTC 2026
% Result : Theorem 3.02s 1.70s
% Output : Refutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 6 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 19 ( 12 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 57 ( 2 ~; 0 |; 6 &; 46 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 28 ( 4 ^; 22 !; 2 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(g_type,type,
g: $tType ).
thf(cGRP_RIGHT_INVERSE_decl,type,
cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
thf(cGRP_RIGHT_UNIT_decl,type,
cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
thf(cGRP_RIGHT_INVERSE_def,definition,
( cGRP_RIGHT_INVERSE
= ( ^ [A: g > g > g,B: g] :
! [C: g] :
? [D: g] :
( ( A @ C @ D )
= B ) ) ) ).
thf(cGRP_RIGHT_UNIT_def,definition,
( cGRP_RIGHT_UNIT
= ( ^ [A: g > g > g,B: g] :
! [C: g] :
( ( A @ C @ B )
= C ) ) ) ).
thf(1,conjecture,
! [A: g > g > g,B: g] :
( ( ! [C: g,D: g,E: g] :
( ( A @ ( A @ E @ C ) @ D )
= ( A @ E @ ( A @ C @ D ) ) )
& ( cGRP_RIGHT_UNIT @ A @ B )
& ( cGRP_RIGHT_INVERSE @ A @ B ) )
=> ! [C: g] :
( ( A @ B @ C )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cE13A2A) ).
thf(2,negated_conjecture,
~ ! [A: g > g > g,B: g] :
( ( ! [C: g,D: g,E: g] :
( ( A @ ( A @ E @ C ) @ D )
= ( A @ E @ ( A @ C @ D ) ) )
& ( cGRP_RIGHT_UNIT @ A @ B )
& ( cGRP_RIGHT_INVERSE @ A @ B ) )
=> ! [C: g] :
( ( A @ B @ C )
= C ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: g > g > g,B: g] :
( ( ! [C: g,D: g,E: g] :
( ( A @ ( A @ E @ C ) @ D )
= ( A @ E @ ( A @ C @ D ) ) )
& ! [C: g] :
( ( A @ C @ B )
= C )
& ! [C: g] :
? [D: g] :
( ( A @ C @ D )
= B ) )
=> ! [C: g] :
( ( A @ B @ C )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG279^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.06 % 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
% 0.10/0.18 % Computer : n012.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 17:35:48 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 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
% 0.83/0.64 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.96/0.78 % [INFO] Parsing done (146ms).
% 0.96/0.80 % [INFO] Running in sequential loop mode.
% 1.52/1.11 % [INFO] eprover registered as external prover.
% 1.52/1.12 % [INFO] Scanning for conjecture ...
% 1.85/1.20 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.85/1.23 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.85/1.23 % [INFO] Problem is higher-order (TPTP THF).
% 1.85/1.23 % [INFO] Type checking passed.
% 1.85/1.23 % [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 ...
% 2.74/1.70 % External prover 'e' found a proof!
% 3.02/1.70 % [INFO] Killing All external provers ...
% 3.02/1.70 % Time passed: 1398ms (effective reasoning time: 897ms)
% 3.02/1.70 % 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)>
% 3.02/1.70 % Axioms used in derivation (0):
% 3.02/1.70 % No. of inferences in proof: 4
% 3.02/1.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1398 ms resp. 897 ms w/o parsing
% 3.02/1.73 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.02/1.73 % [INFO] Killing All external provers ...
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