%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG273^5 : 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 : 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 07:45:07 AM UTC 2026
% Result : Theorem 11.06s 3.63s
% Output : Refutation 11.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of formulae : 11 ( 11 unt; 0 typ; 7 def)
% Number of atoms : 39 ( 21 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 68 ( 2 ~; 0 |; 8 &; 58 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 40 ( 13 ^; 23 !; 4 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(g_type,type,
g: $tType ).
thf(cGROUP2_decl,type,
cGROUP2: ( g > g > g ) > g > $o ).
thf(cGROUP3_decl,type,
cGROUP3: ( g > g > g ) > g > $o ).
thf(cGRP_ASSOC_decl,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(cGRP_LEFT_INVERSE_decl,type,
cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).
thf(cGRP_LEFT_UNIT_decl,type,
cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).
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(cGROUP2_def,definition,
( cGROUP2
= ( ^ [A: g > g > g,B: g] :
( ( cGRP_ASSOC @ A )
& ( cGRP_LEFT_UNIT @ A @ B )
& ( cGRP_LEFT_INVERSE @ A @ B ) ) ) ) ).
thf(cGROUP3_def,definition,
( cGROUP3
= ( ^ [A: g > g > g,B: g] :
( ( cGRP_ASSOC @ A )
& ( cGRP_RIGHT_UNIT @ A @ B )
& ( cGRP_RIGHT_INVERSE @ A @ B ) ) ) ) ).
thf(cGRP_ASSOC_def,definition,
( cGRP_ASSOC
= ( ^ [A: g > g > g] :
! [B: g,C: g,D: g] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) ) ) ) ).
thf(cGRP_LEFT_INVERSE_def,definition,
( cGRP_LEFT_INVERSE
= ( ^ [A: g > g > g,B: g] :
! [C: g] :
? [D: g] :
( ( A @ D @ C )
= B ) ) ) ).
thf(cGRP_LEFT_UNIT_def,definition,
( cGRP_LEFT_UNIT
= ( ^ [A: g > g > g,B: g] :
! [C: g] :
( ( A @ B @ C )
= C ) ) ) ).
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] :
( ( cGROUP2 @ A @ B )
= ( cGROUP3 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEQUIV_02_03) ).
thf(2,negated_conjecture,
~ ! [A: g > g > g,B: g] :
( ( cGROUP2 @ A @ B )
= ( cGROUP3 @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: g > g > g,B: g] :
( ( ! [C: g,D: g,E: g] :
( ( A @ ( A @ C @ D ) @ E )
= ( A @ C @ ( A @ D @ E ) ) )
& ! [C: g] :
( ( A @ B @ C )
= C )
& ! [C: g] :
? [D: g] :
( ( A @ D @ C )
= B ) )
= ( ! [C: g,D: g,E: g] :
( ( A @ ( A @ C @ D ) @ E )
= ( A @ C @ ( A @ D @ E ) ) )
& ! [C: g] :
( ( A @ C @ B )
= C )
& ! [C: g] :
? [D: g] :
( ( A @ C @ D )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(639,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG273^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 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
% 0.13/0.23 % Computer : n010.cluster.edu
% 0.13/0.23 % Model : x86_64 x86_64
% 0.13/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.23 % Memory : 8046.5625MB
% 0.13/0.23 % OS : Linux 6.8.0-71-generic
% 0.13/0.23 % CPULimit : 300
% 0.13/0.23 % WCLimit : 300
% 0.13/0.23 % DateTime : Tue Sep 29 17:36:18 UTC 2026
% 0.13/0.23 % CPUTime :
% 0.13/0.23 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
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/1.01 % [INFO] Parsing done (199ms).
% 1.22/1.02 % [INFO] Running in sequential loop mode.
% 2.09/1.43 % [INFO] eprover registered as external prover.
% 2.09/1.44 % [INFO] Scanning for conjecture ...
% 2.31/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.31/1.58 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.31/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.31/1.58 % [INFO] Type checking passed.
% 2.31/1.59 % [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 ...
% 11.06/3.63 % External prover 'e' found a proof!
% 11.06/3.63 % [INFO] Killing All external provers ...
% 11.06/3.63 % Time passed: 3258ms (effective reasoning time: 2604ms)
% 11.06/3.63 % 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)>
% 11.06/3.63 % Axioms used in derivation (0):
% 11.06/3.63 % No. of inferences in proof: 4
% 11.06/3.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3258 ms resp. 2604 ms w/o parsing
% 11.06/3.67 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.06/3.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------