%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP418-1 : TPTP v9.3.1. Released v2.6.0.
% 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 : n004.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 : Sun Sep 27 07:20:57 AM UTC 2026
% Result : Unsatisfiable 19.51s 9.50s
% Output : Refutation 19.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 2
% Syntax : Number of formulae : 5 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 5 ( 4 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 52 ( 2 ~; 0 |; 0 &; 50 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(a1_decl,type,
a1: $i ).
thf(b1_decl,type,
b1: $i ).
thf(1,negated_conjecture,
( ( a1 @ ( a1 @ inverse @ multiply ) )
!= ( b1 @ ( b1 @ inverse @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
thf(3,plain,
( ( a1 @ ( a1 @ inverse @ multiply ) )
!= ( b1 @ ( b1 @ inverse @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ multiply ) @ ( C @ ( C @ inverse @ multiply ) @ inverse @ ( C @ multiply ) @ inverse @ ( B @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
thf(6,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ multiply ) @ ( C @ ( C @ inverse @ multiply ) @ inverse @ ( C @ multiply ) @ inverse @ ( B @ inverse @ multiply ) @ inverse @ ( A @ multiply ) @ inverse @ multiply ) @ inverse )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(153,plain,
$false,
inference(e,[status(thm)],[3,6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP418-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.10 % 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
% 0.20/0.46 % Computer : n004.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Fri Sep 25 14:53:07 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 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
% 1.44/1.31 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.78/1.57 % [INFO] Parsing done (253ms).
% 1.78/1.59 % [INFO] Running in sequential loop mode.
% 2.88/2.21 % [INFO] eprover registered as external prover.
% 2.88/2.22 % [INFO] Scanning for conjecture ...
% 3.09/2.30 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 3.09/2.33 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 3.09/2.34 % [INFO] Problem is propositional (TPTP CNF).
% 3.09/2.35 % [INFO] Type checking passed.
% 3.09/2.35 % [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 ...
% 19.51/9.50 % External prover 'e' found a proof!
% 19.51/9.50 % [INFO] Killing All external provers ...
% 19.51/9.50 % Time passed: 8823ms (effective reasoning time: 7901ms)
% 19.51/9.50 % Axioms used in derivation (1): single_axiom
% 19.51/9.50 % No. of inferences in proof: 5
% 19.51/9.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8823 ms resp. 7901 ms w/o parsing
% 19.51/9.53 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.51/9.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------